Multi-Source DA has been investigated in previous literature with different aspects to aggregate source datasets. In the popular unsupervised DA, [1]}, [2]}, [3]}, [4]}, [5]} adopted the marginal distribution \(d(\mathcal {S}_t(x),\mathcal {T}(x))\)  of \(\mathcal {H}\) -divergence [6]}, discrepancy [7]} and Wasserstein distance [8]} to estimate domain relations. These works provided theoretical insights through upper bounding the target risk by the source risk, domain discrepancy of \(\mathbb {P}(x)\)  and an un-observable term \(\eta \)  – the optimal risk on all the domains. However, as the counterexample indicates, relying on \(\mathbb {P}(x)\)  does not necessarily select the most related source. Therefore, [9]}, [10]}, [11]} alternatively considered the divergence between two domains with limited target label by using \(\mathcal {Y}\) -discrepancy, which is commonly faced in practice and less focused in theory. However, we empirically show it is still difficult to handle target-shifted sources.
